Answer:
Volume of sphere =
Step-by-step explanation:
We are given that
Radius of sphere=Radius of cylinder=r
Height of sphere=Height of cylinder=h
Height of sphere=h=Diameter of sphere=2r
Volume of cylinder=
Volume of cylinder=
Using the formula
Volume of cylinder=
Volume of sphere=
Using the formula
Volume of sphere=
Hence, the volume of sphere =
Answer: it will take 41 nights for the points he earns with either hotel to be the same.
Step-by-step explanation:
Let x represent the number of nights that it will take for the points he earns with either hotel will be the same.
Hotel Elegance is currently offering 525 points for signing up, plus 35 points for every night Alec books at the hotel. This means that the number of points that Alec will get of he spends x nights at the hotel is
35x + 525
Alternatively, Hotel Paradiso is offering a sign-up bonus of 402 points, plus 38 points per night. This means that the number of points that Alec will get of he spends x nights at the hotel is
38x + 402
For the points to be the same at either hotels, the number of nights would be
35x + 525 = 38x + 402
38x - 35x = 525 - 402
3x = 123
x = 123/3 = 41
Use the quadratic formula and plug in the coefficients

I wasn't able to the plus or minus sign in so I just used the plus sign you can look up the quadratic formula online